In the interview, the 69-year-old Yeltsin also says that Russia is not in dire economic trouble and the America is not the lone superpower.
He also discusses his battle with alcohol and corruption allegations against him and his family. And he takes his successor, Vladmir Putin, to task for mishandling the sinking of the Kursk.
Yeltsin, who became Russia's president in 1991 and survived two armed uprisings by hardline communists, resigned suddenly Dec. 31 after suffering several heart attacks and being hospitalized with pneumonia.
He was also the target of accusations he had accepted bribes. Putin granted Yeltsin lifetime immunity from prosecution upon his resignation.
In the interview with Wallace, Yeltsin insisted his health had improved, that his heart and emotional state were stable, but he did not appear well.
He says he stopped drinking heavily back in 1994 after a heart attack left him noticeably weakened.
He admits he concealed his 1996 heart attack from the public until after the election that year, saying, "I was confident about my health."
The former president, who estimates his net worth at $300,000, denies that he and his family have foreign assets hidden away.
Confronted with statistics showing that the standard of living n Russia had fallen and that suicide, crime and alcoholism were increasing, Yeltsin said, "Your data is wrong. I don't believe your data."
Asked if he believed democracy was firmly established in the new Russia, Yeltsin answered, "Firmly."
He also feels Russia's position in world affairs is rock solid.
"America has not become more influential than Russia. It has not," the former president insisted.
"We have tennis players who knock out American tennis players," he said. "We have female volleyball players who knocked out the American team in straight sets. We have a very high culture - superior to America's."
Yeltsin said that Putin, who served as Yeltsin's prime minister in the last months of his presidency, "is a profound person, a bright personality- very goal-oriented. Once he makes a decision, he'll follow it through."
But Yeltsin admitted than he had to talk to Putin four times to coax him into accepting the presidency. And he said that Putin "isn't decisive enough yet so he needs a couple of years to develop as a leader, for example, in foreign affairs."
Yeltsin also criticized Putin's handling of the sinking of the submarine Kursk in August with 118 sailors aboard. Putin was sharply criticized for remaining on vacation at a Black Sea resort while the rescue operation was under way.
"He made a mistake," Yeltsin said. "He had to be there, or at least in Moscow at that moment."
Putin has also been criticized for jailing media tycoon Vladmir Gusinsky, whose media outlet shad criticized the government, and for hinting at restricting the press.
Yeltsin said part of the advice he gave Putin was "the media must be respected. Its freedom must be defended."
Rarely seen in public since his resignation, Yeltsin has spent most his time at his dacha outside Moscow working on his memoirs. Former premier Mikhail Gorbachev, Yeltsin's predecessor, lives nearby, but he and Yeltsin have not met for years. Yeltsin would not elaborate on the reasons.